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MathGroup Archive 1996

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Re: ts ts ts

  • To: mathgroup at smc.vnet.net
  • Subject: [mg5033] Re: ts ts ts
  • From: Dr Stephen P Luttrell <luttrell at signal.dra.hmg.gb>
  • Date: Sat, 19 Oct 1996 16:40:35 -0400
  • Organization: Defence Research Agency
  • Sender: owner-wri-mathgroup at wolfram.com

Arthur Fritzsche wrote:
> 
> Hi there.
> 
> Does anybody know why Mathematica gets choked trying to solve
> this simple equation? (seems like an easy way to calculate Fourier series up to n=3)
> 
> ---------------------------------
> x1=3
> y1=3
> x2=4
> y2=4
> x3=5
> y3=5
> x4=10
> y4=-20
> x5=11
> y5=30
> x6=12
> y6=-30
> x7=18
> y7=0
> 
> Solve[{
>     y1==a0+a1 Cos[x1]+b1 Sin[x1]+a2 Cos[2 x1]+b2 Sin[2 x1]+a3 Cos[3 x1]+
>         b3 Sin[3 x1],
>     y2==a0+a1 Cos[x2]+b1 Sin[x2]+a2 Cos[2 x2]+b2 Sin[2 x2]+a3 Cos[3 x2]+
>         b3 Sin[3 x2],
>     y3==a0+a1 Cos[x3]+b1 Sin[x3]+a2 Cos[2 x3]+b2 Sin[2 x3]+a3 Cos[3 x3]+
>         b3 Sin[3 x3],
>     y4==a0+a1 Cos[x4]+b1 Sin[x4]+a2 Cos[2 x4]+b2 Sin[2 x4]+a3 Cos[3 x4]+
>         b3 Sin[3 x4],
>     y5==a0+a1 Cos[x5]+b1 Sin[x5]+a2 Cos[2 x5]+b2 Sin[2 x5]+a3 Cos[3 x5]+
>         b3 Sin[3 x5],
>     y6==a0+a1 Cos[x6]+b1 Sin[x6]+a2 Cos[2 x6]+b2 Sin[2 x6]+a3 Cos[3 x6]+
>         b3 Sin[3 x6],
>     y7==a0+a1 Cos[x7]+b1 Sin[x7]+a2 Cos[2 x7]+b2 Sin[2 x7]+a3 Cos[3 x7]+
>         b3 Sin[3 x7]}, {a0, a1, b1, a2, b2, a3, b3}]
> ---------------------------------
> 
> Might there be a more straightforward solution? The sinus and cosinus terms 
>evidently are fixed, so....

You can obtain a quick solution if you wrap your equations in N[], because this 
forces the Sin[] and Cos[] to evaluate to numerical values. Ther solution I then 
obtained was:

{{a0 -> -908.7749999999999, a1 -> -519.642, 
   b1 -> -1411.07, a2 -> 601.6299999999999, 
   b2 -> -506.1069999999999, a3 -> 193.252, 
   b3 -> 129.722}}

-- 
Dr Stephen P Luttrell                  luttrell at signal.dra.hmg.gb
Adaptive Systems Theory                01684-894046 (phone)
Room EX21, Defence Research Agency     01684-894384 (fax)           
Malvern, Worcs, WR14 3PS, U.K.         http://www.dra.hmg.gb/cis5pip/Welcome.html


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